A208830 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..2*n-1} (1 + k*x).

1, 1, 2, 12, 132, 2196, 49836, 1447476, 51542868, 2182001316, 107319488412, 6024315658548, 380536243019220, 26739219616505076, 2070294450495377484, 175215334999701596724, 16099427228106472739988, 1596611582544914141925444, 170028864964367324939511036

Offset

0,3

Comments

Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1 + k*x).

Links

Table of n, a(n) for n=0..18.

Example

 G.f.: 1/(1-x) = 1 + 1*x/(1+x) + 2*x^2/((1+x)*(1+2*x)*(1+3*x)) + 12*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)) + 132*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)*(1+7*x)) +...

Prog

 (PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, 2*k-1, (1+j*x+x*O(x^n)) )), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A208831.

Sequence in context: A200319 A213640 A266489 * A132472 A179420 A346186

Adjacent sequences: A208827 A208828 A208829 * A208831 A208832 A208833

Keyword

nonn

Author

Paul D. Hanna, Mar 01 2012

Status

approved